Recursive Formula

If t1, t2, t3,….,tn,… is a set of series or a sequence. Then a recursive formula for this sequence will be needed to compute all the previous terms and find the value of tn.

tn = tn-1

This formula can also be defined as Arithmetic Sequence Recursive Formula. As you can observe from the sequence itself, it is an arithmetic sequence, which includes the first term followed by other terms and a common difference, d between each term is the number you add or subtract to them.

A recursive function can also be defined for a geometric sequence, where the terms in the sequence have a common factor or common ratio between them. And it can be written as;

tn = r x tn-1

Recursive Function Example:


Let t1=10 and tn= 2tn-1+1

So the series becomes;



t3=2t2+1= 42

And so on…

Register at BYJU’S to learn other mathematical topics in an interesting way.

Practise This Question

A person observes the angle of elevation of the top of a 60m tower from a point on the level ground to be 60. Find the distance between the person and the foot of the tower.